A189375 Expansion of 1/((1-x)^5*(x^3+x^2+x+1)^3).

1, 2, 3, 4, 8, 12, 16, 20, 30, 40, 50, 60, 80, 100, 120, 140, 175, 210, 245, 280, 336, 392, 448, 504, 588, 672, 756, 840, 960, 1080, 1200, 1320, 1485, 1650, 1815, 1980, 2200, 2420, 2640, 2860, 3146, 3432, 3718, 4004, 4368

Offset

0,2

Comments

The Gi1 triangle sums of A139600 lead to the sequence given above, see the formulas. For the definitions of the Gi1 and other triangle sums see A180662.

Links

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 3, -6, 3, 0, -3, 6, -3, 0, 1, -2, 1).

Formula

a(n) = sum(A056594(n-k)*A115269(k), k=0..n).

Gi1(n) = A189375(n-4) - A189375(n-5) - A189375(n-8) + 2*A189375(n-9) with A189375(n)=0 for n <= -1.

a(n) = (2*n^4+56*n^3+538*n^2+2044*n+2469+3*((2*n^2+28*n+89)*(-1)^n+(4*(-1)^((2*n-1+(-1)^n)/4)*(n^2+16*n+57-(n^2+12*n+29)*(-1)^n))))/3072. - Luce ETIENNE, Jun 25 2015

Maple

a:= n-> coeff(series(1/((1-x)^5*(x^3+x^2+x+1)^3), x, n+1), x, n):
seq(a(n), n=0..50);

Mathematica

CoefficientList[Series[1/((1-x)^5(x^3+x^2+x+1)^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -1, 0, 3, -6, 3, 0, -3, 6, -3, 0, 1, -2, 1}, {1, 2, 3, 4, 8, 12, 16, 20, 30, 40, 50, 60, 80, 100}, 50] (* Harvey P. Dale, Dec 05 2014 *)

Crossrefs

Cf. A139600, A189374, A189376.

Sequence in context: A366201 A030073 A115271 * A262975 A062923 A360363

Adjacent sequences: A189372 A189373 A189374 * A189376 A189377 A189378

Keyword

easy,nonn

Author

Johannes W. Meijer, Apr 29 2011

Status

approved